Related papers: Monotonicity - analytic and geometric implications
We study nonlocal elliptic and parabolic equations on $C^{1,\tau}$ open sets in weighted Sobolev spaces, where $\tau\in (0,1)$. The operators we consider are infinitesimal generators of symmetric stable L\'evy processes, whose L\'evy…
In this paper, we show that there is a one-to-one correspondence between operator monotone functions on the nonnegative reals and finite Borel measures on the unit interval. This correspondence appears as an integral representation of…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
For $\mathbb{B}^n$ the $n$-dimensional unit ball and $D_n$ its Siegel unbounded realization, we consider Toeplitz operators acting on weighted Bergman spaces with symbols invariant under the actions of the maximal Abelian subgroups of…
It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite…
We obtain some Poincar\'{e} type formulas, that we use, together with the level set analysis, to detect the one-dimensional symmetry of monotone and stable solutions of possibly degenerate elliptic systems of the form {eqnarray*}…
We study here systems of symmetries on $|1|$--graded parabolic geometries. We are interested in smooth systems of symmetries and we discuss non--flat homogeneous $|1|$--graded geometries. We show the existence of an invariant admissible…
We study the hyperbolic cosine and sine laws in the extended hyperbolic space which contains hyperbolic space as a subset and is an analytic continuation of the hyperbolic space. And we also study the spherical cosine and sine laws in the…
We study relations and characterizations of various elliptic Harnack inequalities for symmetric non-local Dirichlet forms on metric measure spaces. We allow the scaling function be state-dependent and the state space possibly disconnected.…
An open Riemann surface is called parabolic in case every bounded subharmonic function on it reduces to a constant. Several authors introduced seemingly different analogs of this notion for Stein manifolds of arbitrary dimension. In the…
In optimal transport, quadratic regularization is a sparse alternative to entropic regularization: the solution measure tends to have small support. Computational experience suggests that the support decreases monotonically to the…
In \cite{PSMA}, Pal et al. introduced some weighted means and gave some related inequalities by using an approach for operator monotone functions. This paper discusses the construction of these weighted means in a simple and nice setting…
Certain operator-valued functions and new generating structures (instead of generating functionals) are proposed for the analysis of equations for n-point information (n-pi). Some remarks are made concerning the intertwining of linearity…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
We construct a general theory of operator monotonicity and apply it to the Fr\"ohlich polaron hamiltonian. This general theory provides a consistent viewpoint of the Fr\"ohlich model.
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
The focus in this paper is on elliptic homogenization of a certain kind of possibly non-periodic problems. A non-periodic and two-dimensional example is studied, where we numerically illustrate the homogenized matrix.
We show that the topological entropy is monotonic for unimodal interval maps which are obtained from the restriction of quadratic rational maps with real coefficients. This is done by ruling out the existence of certain post-critical curves…
In this paper our aim is to present the completely monotonicity and convexity properties for the Wright function. As consequences of these results, we present some functional inequalities. Moreover, we derive the monotonicity and…
Monotone operator theory and fixed point theory for nonexpansive mappings are central areas in modern nonlinear analysis and optimization. Although these areas are fairly well developed, almost all examples published are based on…